Finiteness of $m$-torsion points in elliptic curves

Question

I'm reading the proof of lemma 1.1.1 (setion VIII) in Silverman's Arithmetic of Elliptic Curves:

I have two questions:

1) Why does he assume that the $m$-torsion subgroup $E[m]$ is finite? Is it obvious? I haven't found any mention of that earlier in the book.

2) Right after the proof he says that lemma 1.1.1 allows the assumption that $E[m]\subset E(K)$. Why?